Answers
Answer:
A = 36√3 - 12π
Step-by-step explanation:
Make 2 identical 30-60-90 triangles out of the "wedge"
For each 30-60-90 triangle:
Since the short leg is 6 the long leg is 6√3
short leg is the base and long leg is the height
a = (1/2)bh
a = (1/2)(6)(6√3)
a = 3(6√3)
a = 18√3
Since there are 2 triangles
a = 36√3
--------------------------------
Then subtract off the area of the 120º sector
a = (120/360)πr^2
a = (1/3)π(6^2)
a = (1/3)π(36)
a = 12π
Shaded area
a = 36√3 - 12π
Step-by-step explanation:
we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).
since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.
basically, the area of a triangle is
1/2 × b×c × sin(A)
A being the angle between the 2 sides b and c. for any 2 sides of the triangle.
one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.
we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.
remember, the sum of all angles in a triangle is 180 degrees.
so, via the law of sines we can then calculate all sides :
a/sin(A) = b/sin(B) = c/sin(C)
with the angles being opposite of the sides.
6/sin(30) = baseline/sin(90)
6/0.5 = baseline/1
12 = baseline
top side² + 6² = 12²
top side² = 12² - 6² = 144 - 36 = 108
top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)
we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.
the area of the 2 triangles is then
6×sqrt(3)×6×sin(90) = 36×sqrt(3)
and the circle segment to be deducted is
pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12
so, the complete answer is
A = 36×sqrt(3) - 12×pi
Related Questions
Which postulate /theorem can you use to prove the two triangles shown are congruent?
Answers
7. Proving the Perpendicular Bisector Theorem Using Reflections
Given: Point P is on the perpendicular bisector m of AB.
Prove: PA PB
Answers
Explanation:
-3-6 is equivalent to 6-(-3). Subtracting a negative number is the same as adding a positive number, so 6-(-3) is the same as 6+3. 6+3 = 9.
What does this graph represent?
Question options:
not moving
acceleration
constant speed
Answers
Answer:
A or C
Step-by-step explanation:
Marie and Amy are cutting ribbons to attach to balloons for Amy's birthday party. Each guest's chair will have on balloon tied to it. each ribbon is 2/3 of a yard and they have 6 yards of ribbon in total. How many ribbons will they cut. A. 1/9 B.4 C.8 D. 9
PLS ANSWER QUICK FIRST RIGHT ANSWER WILL BEE MARKED AS BRAINLEIST
Answers
Answer:
D 9
Step-by-step explanation:
1 ribbon ---- 2/3 yards
x ------ 6 yards
6 * 1 = 2/3 * x
6 = 2/3 x
18/2 = x
x = 9
9 ribbons can be cut from 6 yards of ribbon
In which diagram are angles 1 and 2 vertical angles?
Answers
Answer:
Step-by-step explanation:
can you upload diagram?
Which equation matches the graph shown?
Answers
Answer:
Vertex form: y = -2(x - 1)²
Standard form: y = -2x² + 4x - 2
Step-by-step explanation:
Given the x-intercept as the vertex, (1, 0), and the y-intercept, (0, -2) as the two points on the graph of a parabola:
We can determine the equation by substituting these given values into the vertex form of the quadratic equation:
y = a(x - h)² + k
where:
a = determines the direction of where the graph opens, and the wideness or narrowness of the parabola.
(h, k) = vertex
Solve for the value of a:Use vertex: (1, 0) and y-intercept, (0, -2):
y = a(x - h)² + k
-2 = a(0 - 1)² + 0
-2 = a(-1)²
-2 = a(1)
-2 = a
Quadratic Equation:Vertex form:The quadratic equation in vertex form that matches the graph is:
y = -2(x - 1)² + 0 or y = -2(x - 1)² ⇒ This is the quadratic equation in vertex form.
Standard form:To transform the vertex form into the standard form, y = ax² + bx + c:
Simply expand the perfect square, (x - 1)², through FOIL method before distributing -2:
y = -2(x - 1)²
y = -2(x - 1)(x - 1)
y = -2(x² -2x + 1)
y = -2x² + 4x - 2 ⇒ This is the quadratic equation in standard form.
Lizzy makes $1800 per month working in a nail Spa. And Jackie makes 1500 per month plus 20%
a
percent commission per service per costumer. How many nail services Jackie has to complete per
month in order to make as much as Lizzy does?
Answers
Based on the amount Lizzy makes per month, to reach that amount, Jackie would have to complete 75 nail services.
The difference between Lizzy's base salary and Jackie's is:
= 1,800 - 1,500
= $300
Assuming a nail service costs $20, the amount she makes per service is:
= 20% x 20
= $4
The number of nail services she needs to do is therefore:
= Difference in wages / Amount per service
= 300 / 4
= 75 nail services
In conclusion, Jackie needs to do 75 nail services.
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I don’t know what the answer is
Answers
1-12=-11
Please help explain my answer!!
Why does a compass point towards the earth's geographic North Pole?
My answer:
Because that's where Earth's south magnetic pole is located and they attract.
Make sure to explain your answer.
Help!
Answers
The correct answers are that Earth’s North Pole is close to the magnetic south pole, magnets allowed to move freely align themselves to point north, and the north pole on a compass is attracted to Earth’s south pole. I really hope this helps you!!
An electronics store is having an 18% off sale on everything in the store. To the nearest cent, which of the following could represent regular prices and sale prices of items in the store during the sale? Select all that apply.
Answers
What do I select? You didn't put anything here.
The 18% off on the regular price of $55.43 is $45.45 so (A) is correct and the 18% off on the regular price of $29.99 is $24.59 so (B) is correct rest is not true.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The 18% off of x ⇒ x - (18/100)x = 0.82x
Therefore, 18% off of $55.43 → 0.82 × 55.43 = $45.45
18% off of $29.99 → 0.82 × 29.99 = $24.59
18% off of $215.33→ 0.82 ×215.33 =$172.26
18% off of 849.50 → 0.82 ×849.50 = $679.60
18% off of 652.30→ 0.82 ×652.30 = $534.89
Hence "The 18% off on the regular price of $55.43 is $45.45 and the 18% off on the regular price of $29.99 is $24.59 rest are not true.
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Given question is incomplete,complete question follows ;
An electronics store is having an 18% off sale on everything in the store. To the nearest cent, which of the following could represent regular prices and sale prices of items in the store during the sale? Select all that apply.
Multiple select questions.
A)
regular price: $55.43, sale price: $45.45
B)
regular price: $29.99, sale price: $24.59
C)
regular price: $215.33, sale price: $172.26
D)
regular price: $849.50, sale price: $679.60
E)
regular price: $652.30, sale price: $534.89
how far does the object go
2 hours at 75km\h
Answers
Answer:
150 miles per hourStep-by-step explanation:
Objective: finding the distance
Formula: speed × time = distance
75 × 2 = 150
final answer: 150 mph
Using the appropriate Algebraic identity evaluate the following:(3p -q) (3p +q)
Answers
Step-by-step explanation:
expand and multiply the terms
This is probably easy oh well
Answers
I really don’t know how to do this
Answers
(16/25)^2= 1- (26/5)^2/a^2
256/625=1- 676/25a^2
676/25a^2=1- 256/625
676/25a^2=369/625
422500=9225a^2
a^2 = 16900/369
a= 6.76753
= 6.8
D is the answer
Nina paid $37.57 for 13 gallons of gas Fred paid $55.67 for 19 gallons of gas Eleanor paid $48.62 for 17 gallons of gas. Who got the best buy?
(Find the unit price for each
Answers
Answer:
Nina paid $2.89 per gallon.
Fred paid $2.93 per gallon.
Elanor paid $2.86 per gallon.
Elanor got the best deal.
Step-by-step explanation: Simple division, and if you don't know how to, just learn it or use a calculator.
Answer:
Eleanor because they paid the lowest.
Step-by-step explanation:
N=Nina F=Fred E=Eleanor
N 37.57/13=2.89 per gallon
F 55.67/19=2.93 per gallon
E 48.62/17=2.86 per gallon
jerry has 3,572 live chickens in his poultry farm.if there are 38 boxes , how many chickens must go in each box?
Answers
Answer: 94 live chickens go in each box.
Step-by-step explanation: 3,572 divided by 38 = 94 so 94 live chickens go in each box.
hope this helps :)
[tex]at a school of 1050 pupils exactly 4% are absent on a particular day.how many are present.[/tex]
at a school of 1050 pupils exactly 4% are absent on a particular day.how many are present.
Answers
The price of oranges is proportional to the number of oranges if
One orange costs 1200 Rs. Find:
A. The price of 12 oranges.
B. The amount of oranges that cost 32,000 Rs.
Answers
#1
Cost of 1orange=1200
Cost of 12 oranges:-
[tex]\\ \sf\longmapsto 1200(12)=14400[/tex]
#2
Total cost=32000Cost of one orange=1200Total oranges
[tex]\\ \sf\longmapsto 32000\div 1200[/tex]
[tex]\\ \sf\longmapsto 2666.6[/tex]
[tex]\\ \sf\longmapsto 2667[/tex]
[tex]\sqrt{7+2\sqrt{10} } -\sqrt{7-2\sqrt{10} }[/tex]
Answers
What is the slope-intercept form of the linear equation 2x - 8y = 32?
(Don't forget to simplify fractions if possible)
Answers
Answer:
y = 1/4x + 4
Step-by-step explanation:
2x - 8y = 32
-2x -2x
-8y = -2x + 32
divide everything by -8
so that y becomes positive
answer : Y = 1/4x + 4
The slope-intercept form of the linear equation 2x - 8y = 32 is y = (1/4)x - 4.
Given is an equation of a line 2x - 8y = 32, we need to convert it into slope-intercept form of the linear equation.
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To convert the equation 2x - 8y = 32 into slope-intercept form, we need to isolate y on one side of the equation.
Let's rearrange the given equation to solve for y:
2x - 8y = 32
Subtract 2x from both sides:
-8y = -2x + 32
Divide both sides by -8:
y = (2/8)x - 4
Simplifying further, we get:
y = (1/4)x - 4
So, the slope-intercept form of the linear equation 2x - 8y = 32 is y = (1/4)x - 4.
Learn more about linear equation click;
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If f(x)=6, what is x?
Answers
Answer:so: 6=6/5-x^3
6=6(5-x^3)
6=30-6x^3
-6x^3=6-30
-6x^3=-24
-6x^3+24=0
6x^3-24=0
6(x^3-4)=0
x^3-4=0
x^3=4
x=cube root 4
x=1.5874
Step-by-step explanation:
A car was traveling at 25 m/s when it slammed on the brakes and came to a complete stop in 3 seconds. What is the cars INITIAL/FINAL VELOCITY?
Answers
Answer:
Initial velocity = 25 m/s
Final velocity = 0 m/s
Step-by-step explanation:
Initial velocity is the speed in the beginning and final velocity is the speed in the end.
The problem says the car was traveling at 25 m/s, so that is the initial velocity. The end of the problem states the car came to a complete stop after 3 seconds. Therefore, the final velocity is 0 m/s.
Please find x and y... I will mark you brainliest
Answers
Answer:
Step-by-step explanation:
Dodoodo
Step-by-step explanation:
x=30 and y=30. I have solve it. See the picture that I have attached.
The coefficient in the formula above tells us that there are?
Answers
Answer: srry if im wrong but i think it is Answer:1.A ____ is like a recipe for a chemical substance. (valence, formula, subscript, coefficient)
Step-by-step explanation:
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 80 meters × 60 meters. How much shorter is the route across the park than the route around its edges?
Answers
Answer:
40meters
Step-by-step explanation:
rectangular park has 90 degree at vertex.so
in that right angled triangle
we have,
length=base=80meters
breadth=perpendicular=60
diagonal=hypotenuse=?
now,
h^2=p^2+b^2
h=square root under 80^2+60^2
h=square root under 6400+3600
h=square root under 10000
h=100
Again,
around root =80+60=140
daigonal=100.
so
the route is 140-100=40meters shorter
answer this asap
1)There are 30 students in a class. 18 are girls. Express the number of girls as a percentage of the
class.
2)What is the probability of choosing the color blue from the colors of the rainbow?
Answers
Answer:
1) 18/30×100%=60%
Hope this helps!!!
Answer:
See below
Step-by-step explanation:
Hi there!
Question 1
There are 30 students in total and 18 are girls, making 18/30 of the class girls. To express this as a percent, divide, then multiply by 100:
18/30 = 0.6
0.6 × 100 = 60%
Therefore, 60% of the class is girls.
Question 2
There are 7 colours in the rainbow, making blue 1/7 of the colours of the rainbow.
Therefore, the probability of choosing blue from the colours of the rainbow is 1/7.
I hope this helps!
Two cyclists are 7 miles apart when they begin biking away from each other in
opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of
the second cyclist is b miles per hour greater than the speed of the first cyclist.
How many miles apart are the cyclists in 45 minutes
Answers
Answer:
25
Step-by-step explanation:
Its just 25
find the slope of the line, given the points (0,2) and (3.6,2) show all your work
Answers
Answer:
There is no slope because the slope is zero. The line has no slope because it's a vertical line.
Step-by-step explanation:
Slope = [tex]\frac{2-2}{3.6-0} = \frac{0}{3.6} =0[/tex]
Slope = 0
The line has no slope.
I believe you should get 0 as your slope.
solve pls brainliest
Answers
Answer:
192
Step-by-step explanation:
Volume of a rectangular prism = length times width times height.
For the following prism, length = 4, width = 6 and height = 8
So volume would equal 4 * 6 * 8 = 192ft²
What is the graph of y=3/4x-3
Answers
Answer:
the answer is graph C
Step-by-step explanation:
babyface_wee
Answer: Graph A
Step-by-step explanation:
y-intercept = -3 So, Not Graph B
Slope = 3/4x = rise 3 run 4 or up 3 right 4. So not Graph C
Graph A meats all the criterias.